Study of a new method for high energy top tagging at the ATLAS experiment

Scuola di Scienze

Corso di Laurea Magistrale in Fisica

STUDY OF A NEW METHOD

FOR HIGH ENERGY

TOP TAGGING

AT THE ATLAS EXPERIMENT

Relatore:

Prof. Nicola Semprini Cesari

Correlatore:

Dott. Roberto Spighi

Presentata da:

Camilla Vittori

Sessione II

teresse nella sica delle particelle. Lo scopo di questa tesi è la ricostruzione di top adronici con un alto impulso trasverso (boosted) attraverso il Template Overlap Method (TOM). A causa dell'alta energia, i prodotti di decadimento dei boosted top sono parzialmente o totalmente sovrapposti e risultano con-tenuti in un singolo jet di grandi dimensioni (fat-jet). Il TOM confronta le distribuzioni di energia del fat-jet con campioni di top ottenuti con simulazioni Monte Carlo (template). L'algoritmo è basato sulla denizione di una fun-zione di overlap, che quantica il livello di accordo tra il fat-jet e il template, consentendo un'eciente discriminazione del segnale dai contributi di fondo. Per ottenere un'ecienza sul segnale attorno al 90% e una corrispondente reiezione dal fondo del 70%, è stato necessario stabilire un punto di lavoro. Le performance del TOM sono state testate su campioni MC nel canale muonico e confrontate con i metodi presenti in letteratura. Tali metodi saranno inseriti in un'analisi multivariata al ne di creare un metodo di tagging globale che sarà incluso nella misura della sezione d'urto dierenziale della produzione di coppie t¯t sui dati acquisiti nel 2012 a √s=8 TeV, nella regione dello spazio delle fasi in cui potrebbero essere possibili processi di nuova sica. A causa della sua caratteristica di aumentare l'ecienza di identicazione all'aumento del pT, il Template Overlap Method giocherà un ruolo fondamentale durante la

prossima presa dati a √s=13 TeV, dove quasi la totalità dei top sarà prodotta ad alta energia, rendendo impossibile l'identicazione con le tecniche standard.

in particle physics. The aim of this thesis is the reconstruction of hadronic top with high transverse momentum (boosted) with the Template Overlap Method (TOM). Because of the high energy, the decay products of boosted tops are partially or totally overlapped and thus they are contained in a single large radius jet (fat-jet). TOM compares the internal energy distributions of the candidate fat-jet to a sample of tops obtained by a MC simulation (tem-plate). The algorithm is based on the denition of an overlap function, which quanties the level of agreement between the fat-jet and the template, allo-wing an ecient discrimination of signal from the background contributions. A working point has been decided in order to obtain a signal eciency close to 90% and a corresponding background rejection at 70%. TOM performances have been tested on MC samples in the muon channel and compared with the previous methods present in literature. All the methods will be merged in a multivariate analysis to give a global top tagging which will be included in the measurement of the t¯t production dierential cross section performed on the data acquired in 2012 at √s=8 TeV in high phase space region, where new physics processes could be possible. Due to its peculiarity to increase the identication eciency with respect the top pT, the Template Overlap Method

will play a crucial role in the next data taking at √s=13 TeV, where the al-most totality of the tops will be produced at high energy, making the standard reconstruction methods inecient.

Introduzione 1

1 Top quark physics 3

1.1 The Standard Model . . . 3

1.1.1 The electromagnetic interaction . . . 6

1.1.2 The weak interaction . . . 9

1.1.3 The strong interaction . . . 11

1.2 The top quark . . . 14

1.2.1 Top pair production . . . 15

1.2.2 Single top production . . . 16

1.2.3 Top decay . . . 18

1.2.4 Top quark mass . . . 21

1.3 Cross section measurements . . . 22

1.3.1 t¯t total cross section . . . 24

1.3.2 Dierential cross section . . . 25

1.4 Beyond Standard Model . . . 26

2 LHC and ATLAS 31 2.1 LHC . . . 31

2.2 ATLAS . . . 34

2.2.1 The magnets system . . . 36

2.2.2 Inner Detector . . . 38

2.2.3 Calorimetric System . . . 41

2.2.4 Muon Spectrometer . . . 44 ii

2.2.5 The Trigger and Acquisition System . . . 46

2.2.6 LUCID . . . 48

3 Top Reconstruction and Selection 51 3.1 Top Reconstruction . . . 51

3.1.1 Jets . . . 52

3.1.2 Leptons . . . 56

3.1.3 Neutrinos . . . 60

3.2 Boosted top reconstruction . . . 61

3.3 Jet Grooming Techniques . . . 64

3.3.1 Mass-drop ltering . . . 65

3.3.2 Trimming . . . 66

3.3.3 Pruning . . . 67

3.4 Top tagging techniques . . . 67

3.4.1 Jet Mass . . . 67

3.4.2 Splitting Scale . . . 69

3.4.3 N-Subjettiness . . . 69

3.4.4 HepTop Tagger . . . 70

3.4.5 Template Overlap Method . . . 72

3.5 Data and Monte Carlo Samples . . . 79

3.5.1 Data sample . . . 79

3.5.2 Monte Carlo simulation . . . 79

4 Results 83 4.1 Selection Criteria . . . 83

4.2 Data Monte Carlo Comparison . . . 85

4.3 TOM Results . . . 94

4.4 TOM Systematics . . . 100

1.1 The fundamental fermions and bosons of the Standard Model. . . 6 1.2 Feynman diagrams of the fundamental QED vertex (top right), the

e+e− annihilation (top left), the emission of a photon by a positron (bottom right) and the couple creation by a photon (top left). All of these diagrams can be obtained through the fundamental vertex. . . 8 1.3 Fundamental vertexes of the weak interaction in both charged current

CC (top) and neutral current (bottom). . . 9 1.4 Comparison between electromagnetic and strong coupling constants. 13 1.5 Feynman QCD diagrams: from the right the exchange of a gluon by

two quarks and triplet and quartic gluon self-interactions are shown. 14 1.6 Gluon-gluon fusion and quark-antiquark annihilation Feynman

dia-grams for t¯t production at leading order QCD. . . 16 1.7 Theoretical Inclusive t¯t production cross section predicted for LHC

and comparison between ATLAS, CMS, D0 and CDF measurements. LHC energy 4 times greater than that of the Tevatron corresponds to a top pair cross section 30 times greater [15]. . . 17 1.8 Leading-order Feynman diagrams for s-channel, t-channel and

asso-ciated production with W boson. . . 18 1.9 Illustration of dierent top pair production and decay modes. . . 20 1.10 Top pair decay channels (right) and the corresponding

branching-ratios (left). . . 21 1.11 Overview of the top mass measurements from both ATLAS and CMS

in the lepton+jets, dileptonic and hadronic channels [12]. . . 22

1.12 Summary of the ATLAS and CMS most precise measurements of top-antitop pair per decay mode, compared with several theory

pre-dictions at NLO and NNLO QCD [2]. . . 25

1.13 Lepton+jets channel normalised dierential t¯t production cross sec-tion obtained by the ATLAS collaborasec-tion as a funcsec-tion of Mt¯t, pT ,t¯t and yt¯t. The measurements is compared to the NLO prediction from MCFM [18]. . . 27

2.1 Schematic view of CERN accelerators. . . 33

2.2 The ATLAS detector. . . 35

2.3 Section of ATLAS detector. . . 36

2.4 The Central Solenoid (blue), the Barrel Toroid and the End-Cap Toroids (red) of the magnetic system. . . 37

2.5 An illustration of the ATLAS Inner Detector. It highlights the major features of the design, showing the arrangement of modules in the barrel and end-caps of the Pixel Detector, the SCT and the TRT. . . 39

2.6 cross sectional view of the Inner Detector. . . 40

2.7 The ATLAS calorimetric system. . . 42

2.8 ATLAS Muon Spectrometer layout. . . 45

2.9 Schematic diagram of ATLAS trigger system. . . 47

2.10 LUCID detector under construction in view of the II Run of LHC. . 49

3.1 A sample parton level event, together with soft contributions, clus-tered with four dierent jet algorithms, illustrating the active catch-ment areas of the resulting hard jets [31]. . . 55

3.2 Electron identication eciency with increasing number of primary vertices and pile-up, for dierent eciency values [35]. . . 58

3.3 Stability of muon isolation eciency with increasing number of pri-mary vertices, for combined muons [38]. . . 59

3.4 The four kinds of muon candidates in ATLAS: combined, standalone, segment-tagged and calo-tagged muons. . . 60

3.5 Comparison between data and simulation of Emiss

T (letf ) and Exmiss,

E_ymiss (right) resolutions as a function of the number of primary vertices [39]. . . 62 3.6 (a) The opening angle between the W boson and b quark in top

decays (t → W b) as a function of the top pT in simulated PYTHIA

events. (b) The opening angle of the W → q¯q process from top decays as a function of the pW

T . Both distribution are at the particle

level [41]. . . 63 3.7 Graphical representation of jets produced in a top decay event in

case of low (left) and high (centre) values of top pT. On the right

there is the high top pT conguration reconstructed using a large-R

jet. . . 64 3.8 A representation of the trimming procedure. . . 66 3.9 Comparison of POWHEG Z0

→ t¯tsignal to multi-jet background as a function of jet mass and of splitting scale √d12 in the range 6006

pjet_T 6800 GeV. The dotted lines show the ungroomed jet distribution, while the solid lines show the corresponding trimmed (fcut=0.05 and

Rsub =0.3) jets. The distributions are reconstructed both with the

anti-kt (left) and C/A (right) algorithms. . . 68

3.10 A representation of the HepTop Tagger algorithm chain. . . 71 3.11 Distribution of the E, pT, φ and η variables of the top template.. . . 75

3.12 Distribution of E, pT, φ and η variables of the W boson coming from

the decay of the generated top. E, pT and η are represented in a

logarithmic scale. . . 76 3.13 Distribution of E, pT, φ and η variables of the b quark coming from

the decay of the generated top. E, pT and η are represented in a

logarithmic scale. . . 77 3.14 Distribution of E, pT, φ and η variables of one of the two quarks

produced from the W boson decay (analogue trend for the other quark). E, pT and η are represented in a logarithmic scale. . . 78

4.1 An illustration of the top pair event topology decaying to lepton+jets channel. . . 85 4.2 Comparison between Monte Carlo and data distribution in the

analy-sis of the pT, η and φ kinematic quantities of the hadronic top quark

in the muon channel. Real data are represented with black dots, while Monte Carlo samples have dierent colours on the basis of their origin. Diboson, Z+jets, QCD, Single top, t¯t dilepton, W+jets, t¯tuntruth-matched background samples have been considered. The same legend has been used in all the following plots. . . 87 4.3 Comparison between Monte Carlo and data distribution in the

anal-ysis of the pT, η and φ kinematic quantities of the muon. . . 88

4.4 Comparison between Monte Carlo and data in the analysis of the overlap distribution in the muon channel. On the bottom there is an expansion of the lower part of the plot.. . . 89 4.5 Comparison between Monte Carlo and data distribution in the

anal-ysis of the number of b-jets and Emiss

t in the muon channel. . . 90

4.6 Comparison between Monte Carlo and data distribution in the anal-ysis of the pT, η and φ kinematic quantities of the electron. . . 92

4.7 Comparison between Monte Carlo and data in the analysis of the overlap distribution in the electron channel. On the bottom there is an expansion of the lower part of the plot. . . 93 4.8 Overlap distribution for Monte Carlo t¯t signal (top) and QCD

back-ground (bottom). . . 95 4.9 Distributions of t¯tsignal (top) eciency and QCD background

rejec-tion (bottom) as a funcrejec-tion of the overlap. . . 96 4.10 Comparison of the simulated fat-jet tagging eciency and fat-jet

light quark/gluon rejection [62]. . . 97 4.11 Distribution of the QCD rejection as a function of the t¯t eciency.

The rejection is represented in a logarithmic scale. . . 98 4.12 Comparison between the TOM performances with the other top

4.13 Overlap distribution as a function of the hadronic top momentum. . 99 4.14 Overlap distribution as a function of pile-up for t¯t signal events. . . . 100 4.15 Distribution of the eciency average value for each systematic. . . . 101

1.1 Standard Model leptons . . . 4 1.2 Standard Model quarks . . . 5 1.3 Standard Model gauge bosons . . . 5 1.4 Expected single top quark production cross sections in dierent

chan-nels at a center-of-mass energy of 7 TeV and 8 TeV, given by approx-imate NNLO assuming mt= 172.5 GeV [2]. . . 18

1.5 Summary of main signatures and background of the three t¯t decay channels. . . 20 2.1 LHC technical parameters for 2012. . . 32 2.2 Nominal detector performances for the ATLAS calorimetric system

[21].. . . 42 3.1 Cross Section used in Monte Carlo production for signal and

back-ground samples. The cross section values reported involve only the semileptonic and dileptonic top decay channels. The number of QCD and dileptonic processes will be considerably reduced with the anal-ysis cut application. . . 81 4.1 Summary of Monte Carlo and data number of event calculated in

respect to the pT distribution of the hadronic top with an overlap

value greater than 0.7 in the muon channel. . . 91

With unprecedented high center-of-mass energy and luminosity, LHC provided an important development in the study of top quark, allowing to perform high-statistic measurements. Since its discovery, the study of the top quark has represented one of the most investigated eld in particles physics, because of its peculiar properties, as the largest mass and the smallest decay time, that oer the unique possibility to study a bare quark.

The analysis presented in this thesis is focused on the reconstruction of the hadronic top decay (t → W b → qq0

b) at high momentum; the results of this study will improve the measurement of the t¯t production dierential cross section, performed on data collected by the ATLAS detector on 2012.

At high energy (pT>300 GeV), the decay products of hadronic top quarks

are so collimated that the standard reconstruction techniques begin to fail because the separation among the three emitted jets becomes negligible and they tend to be superimposed in a single, energetic and large radius jet (fat-jet). The aim of this analysis is to reconstruct high energy top quarks with the Template Overlap Method (TOM), a new procedure, still not applied in the standard analysis, specially optimized for hadronic top decays.

TOM performances have been evaluated on MC samples in the muon channel; the method has provided similar performances compared with the published results of previous techniques. At the moment, a working point has been chosen in order to have a signal eciency of about 90% and a background rejection of about 70%.

An important TOM feature is the increase of the eciency with the top pT,

that is crucial for two reasons: rst, it permits to study top produced in high momentum phase space region with the data acquired at √s= 8 TeV, where eventual processes coming from new physics are expected; second, it allows to reconstruct the top acquired in the next data taking at √s= 13 TeV, where the almost totality of them will be produced at high energy and the standard reconstruction will be not ecient.

The structure of the thesis is the following. In Chapter I a description of the Standard Model with particular attention to top quark features is presented. A synthetic panorama of the ATLAS detector is given in Chapter II in order to have a better comparison of the following analysis. A detailed description of the Template Overlap Method is provided in Chapter III, associated to a comparison with the other boosted top tagging algorithms. In Chapter IV the obtained results of the Template Overlap Method together with its systematics and the comparison with previous results are presented. In the end, the Conclusions.

Top quark physics

1.1 The Standard Model

Developed in the early 1970s, the Standard Model (SM) is the theory which successfully describes the fundamental particles and the interactions among them (see Fig.1.1) in the language of grand unication theory. The SM forces involving fundamental particles are the electromagnetic, the weak and the strong interactions, while, until now, it as not been possible to construct a consistent theory of the gravitational interaction.

According to the strong force, the ultimate constituents of matter are divided into leptons and quarks, all point-like fermions with spin 1/2 [1]. On the basis of the weak interaction, leptons and quarks are both divided into three weak isospin doublets (see Tab.1.1 and 1.2), each one consisting of a massive charged particle (e, µ and τ) and the corresponding neutrino (νe, νµ and ντ).

 e νe  µ νµ  τ ντ 

While electron was known from the end of XIX century, the muon, considered an unstable heavy electron, was the rst particle not involved in the structure of ordinary matter to be discovered (observed in cosmic rays in 1937). Tau was rst revealed in accelerator experiments in 1974 and neutrino, after been

predicted by Pauli's theory, was nally found in beta decay in the 1950s [1]. Particles are identied by quantum numbers thus, for instance, to leptons corresponds the leptonic number L conserved by all the interactions. Each weak doublet is described by leptonic number Le, Lµand Lτ, approximatively

conserved by all the interactions. In Tab.1.1 a summary of all lepton quantum numbers have been listed together with a quotation of neutrino mass superior limits [2].

Table 1.1: Standard Model leptons

Lepton Q (|e|) L Le Lµ Lτ Mass (MeV/c2)

e -1 +1 1 0 0 0,511 νe 0 +1 1 0 0 < 2,2 10−6 µ -1 +1 0 1 0 105,65 νµ 0 +1 0 1 0 < 0.19 τ -1 +1 0 0 1 1777,82 ντ 0 +1 0 0 1 < 18,2

Quarks occur in six dierent avours, represented by the assignment of quan-tum numbers labeled u, d, c, s, t, b (see Fig.1.1). Because of the similarity between up and down mass values, these two quarks are grouped in a strong isospin doublet (I = 1/2, with I3 = ±1/2as third component). While leptons

carry an integer charge value (0 or ±1|e|), quarks carry fractional charge; each weak doublet of quarks contains a quark with charge +2/3|e| and another one with charge −1/3|e|.

 u d  c s  t b 

Because of connement, the property of the strong interaction which force quarks bound in hadrons, quarks cannot exist as free particles. All the ob-served hadrons are quark-antiquark (mesons) or quark-quark-quark (baryons) combinations. To all quarks an additional quantum number is associated, the

baryon number, conserved by all the interactions, whose value is 1/3 (−1/3 for anti-quarks and 0 for leptons). The quark quantum numbers are listed in Tab.1.2 [2].

Table 1.2: Standard Model quarks

Quark Q (|e|) I I3 C S T B Mass (GeV/c2)

u +2/3 1/2 +1/2 0 0 0 0 2,3 ·10−3 d -1/3 1/2 -1/2 0 0 0 0 4,8 ·10−3 c +2/3 0 0 1 0 0 0 1,275 s -1/3 0 0 0 1 0 0 95 ·10−3 t +2/3 0 0 0 0 1 0 173,07 b -1/3 0 0 0 0 0 1 4,18

In order to understand certain properties of hadrons is necessary to intro-duce for each avour the colour charge, which can assume three possible values: red, blue and green. Considering that to each particle corresponds an antipar-ticle, with opposite quantum numbers, the total number of the fundamental particles allowed in the Standard Model amounts to

[6(leptons) + 6(quarks) × 3(colours)] × 2 = 48 .

Table 1.3: Standard Model gauge bosons

Force Gauge boson Q (|e|) Mass (GeV/c2₎

Strong gluon (g) 0 0 Electromagnetic photon (γ) 0 0

Weak W± ±1 80,385 ± 0,015 Weak Z0 0 91,1876 ± 0,0021

In the Standard Model, particles interact with each other by coupling with specic elds whose quanta are spin-1 particles (bosons [2]). The eld quanta of electromagnetic, weak and strong forces are respectively the photon γ, three massive particles W+_{, W}− _{and Z}0 _{and eight gluons (see Tab.1.3). Of these,}

Figure 1.1: The fundamental fermions and bosons of the Standard Model.

only W± _{and Z}0 _{have mass because of the interaction with the Higgs eld,}

a property which ensures the typical short range of the weak interaction. Charged leptons can interact through both the electromagnetic and the weak forces, while quarks, which are coloured particles, are aected by the strong interaction too, otherwise neutrino can interact only through the weak force. In order to show the relative magnitudes of the fundamental forces, the strong interaction amplitude has been xed to 1 and all the other are refereed to it:

Strong Electromagnetic Weak Gravitational 1 10−2 10−7 10−39 .

Fig.1.1 illustrates all particles allowed in the Standard Model, including gauge bosons.

1.1.1 The electromagnetic interaction

Described by quantum eld theories, all the Standard Model interactions arise from the coupling between particles and elds. The intensity of the intera-ctions is described by coupling constants, which enter in the matrix element of

each process [3]. In the SM, the structure of the dierent interactions is deter-mined by a symmetry principle requiring that the corresponding Lagrangian is invariant under local gauge transformations. In this way, all the terms of the Lagrangian can be generated starting from the known term of the free material particle.

In the specic case of the electromagnetic interaction, the coupling of charged particles with the electromagnetic eld is due to the electric charge. The quan-tum eld theory describing this interaction is the Quanquan-tum Electrodynamics (QED) [4], symmetric with respect gauge rotation of U(1) group. The QED coupling constant is called ne-constant, a dimensionless quantity dened as

αe =

e2

4π0~c

= 1

137 , (1.1)

where e is the electric charge. The coupling constant is a function of energy and for this reason it is called "running". According to quantum eld theory, in the vacuum medium photon emission, pair annihilation and pair creation phenomena happen continuously: this eect is called vacuum polarization. If a charged sphere is present, the e+_e−_{pairs become oriented, forming a virtual}

cloud around the charged body. The net eect is a screening of the sphere and thus a gradually reduction of the power of its charge at increasing distance from it. In this ideal experiment, the distance of closest approach of a probe to the charge is a decreasing function of the energy of the probe: consequently, high-energy probes will see a larger charge on the sphere.

The QED Lagrangian can be obtained from the free Dirac Lagrangian: Lf ree = ¯ψ(iγµ∂µ− m)ψ , (1.2)

requiring the invariance under global and local gauge transformation in the electric charge space. The invariance under a global phase rotation, which is a continuous symmetry, through the Noether's theorem, leads to the con-servation of the electric charge (e = √4παe). Generalizing the global phase

symmetry to a local one, allows to pass from a theory describing free particles to a theory in which particles experience electromagnetic interaction. In order

to preserve Lagrangian invariance under local gauge rotation, the introduction of the gauge covariant derivative is necessary

∂µ→Dµ = ∂µ+ iqAµ(x) , (1.3)

where the quanta of the vector eld Aµ is the photon. The free-particle

La-grangian of Eq.(1.2) is replaced by the locally gauge-invariant expression LQED =Lf ree− JµAµ−

1 4FµνF

µν _{, (1.4)}

which is indeed the QED Lagrangian. In Eq.(1.4) Jµ _{is the conserved}

electro-magnetic current and the last term represents the propagation of free photons, in which Fµν is the Maxwell's electromagnetic tensor (Fµν = ∂µAν − ∂νAµ).

A photon mass term with the form Lγ =

1 2m

2_Aµ_A

µ is not present in the

expression of the QED Lagrangian because it would violate the local gauge invariance: this leads to the existence of massless photon.

Figure 1.2: Feynman diagrams of the fundamental QED vertex (top right), the e+e− annihilation (top left), the emission of a photon by a positron (bottom right) and the couple creation by a photon (top left). All of these diagrams can be obtained through the fundamental vertex.

1.1.2 The weak interaction

The weak interaction takes place between all fundamental particles of the Standard Model. Because of the small strength of this force compared to electromagnetic and strong ones, weak interactions are observable only when the other forces cannot occur. The quantum eld theory describing the weak interaction alone is often called Quantum Flavordynamics (QFD) [4], symmet-ric with respect gauge rotation of SU(2)L group (SU(2)L indicates that only

left-handed particles can couple with the weak eld). Three vector bosons mediate this interaction, two are electrically charged, W+ _{and W}−_{, each the}

antiparticle of the other, and one is neutral, Z0. In the weak interaction vertex

two particles interact exchanging a vector boson: if it is a W, the charges of fermions in the nal and initial states dier by a unit and the process is called charge current interaction (CC), if it is the Z, the two electric charges are equal and the process is labelled as neutral current interaction (NC). Fig.1.3 shows the fundamental vertexes of the weak interaction.

Figure 1.3: Fundamental vertexes of the weak interaction in both charged current CC (top) and neutral current (bottom).

The weak interaction was rst observed in the process of β decay

n → p + e−+ νe (1.5)

appro-ximation, successful at low momentum transferred (q2 _{<< M}2

W), the virtual

W boson exchanged was neglected and the decay was described by the Fermi coupling constant GF = g2/MW2 , where g2 is the weak charge. With the use

of Fermi's approximation, it has been possible to measure the rates of lots of weak decays and to verify that they have the same coupling: this leads to the development of the weak coupling universality concept [1]. Fermi's phenomenological description of weak interaction was based on the similarity with the electromagnetic one; in order to improve the analogy it is important to leave the eective theory and to introduce the presence of a vector boson. The latter must carry charge ±1|e| or 0, be enough massive to explain the short range of this force and with indenite parity. In addiction, in order to involve the violation of parity and the coupling to left-handed particles ΨL = 1₂(1 − γ5)Ψ only, the structure of the weak interaction must be of type

V-A (vector-axial vector).

Experimentally, decays into fermions belonging to the same weak doublet are found to be more frequent, although universality requires the corresponding matrix elements to be equal. In 1963 Cabibbo proposed the solution to this problem [5]. He assumed that d- and s-quark states participating in the weak interactions are rotated by a mixing angle θC, called "Cabibbo mixing angle"

 u d0  =  u d cosθC+ s sinθC  . (1.6)

The same procedure can be applied to all the quark families. Therefore one can conclude that the eigenstates of the weak interaction do not coincide with the mass eigenstates, but are rotated by a unitary 3 × 3 matrix, called Cabibbo-Kobaiashi-Maskawa (CKM) matrix. The quark mixing transformation is:

    d0 s0 b0     =     Vud Vus Vub Vcd Vcs Vcb Vtd Vts Vtb         d s b     . (1.7)

been experimentally determined [2]:   Vud= 0, 97427 ± 0, 00015 Vus= 0, 22534 ± 0, 00065 Vub= 0, 00351+0.00015−0.00014 Vcd= 0, 22520 ± 0, 00065 Vcs= 0.97344 ± 0.00016 Vcb= 0.0412+0.0011−0.0005 Vtd= 0, 00867+0.00029_−0.00031 Vts= 0.0404+0.0011_−0.0005 Vtb= 0.999146+0.000021_−0.000046   . The o-diagonal values are small, therefore the corresponding mixing angles are small, while the diagonal elements are close to 1, meaning that the most favoured transitions are those happening among quarks that come from the same isospin doublet. Indeed the model predicts a specic sequence of decays: the top quark, for example, decays mostly t → W+_b.

In 1967-1968 Weinberg and Salam proposed a gauge theory unifying weak and electromagnetic interactions, the so called electroweak interaction [6]. This force is based on the SU(2) group of weak isospin T and the U(1) group of weak ipercharge, with four generators and four massless gauge elds; both of them are connected with the electromagnetic charge Q by the relation

Q = T3+

1

2Y , (1.8)

where T3 is the third component of the weak isospin. The electroweak

uni-cation conserves the local gauge invariance, nevertheless it describes W and Z0 as massless bosons, while they are massive particles, as proved by experi-ments. Through the introduction of the Higgs mechanism it is possible to preserve the local gauge invariance and to give mass to the vector boson of the weak interaction, keeping the photon massless. Predicted in 1960s as the main responsible of the electroweak symmetry breaking, the Higgs boson was nally discovered on 4 July 2012, with a mass around 125 GeV/c2 _[7].

1.1.3 The strong interaction

The strong interaction describes the interactions among quarks and gluons and how they bind together to form hadrons. Quantum Chromodynamics (QCD) [8] is the quantum eld theory of the strong interactions, symmetric with respect gauge rotation of SU(3) group. The coupling magnitude can be estimated, from the decay probability of unstable hadrons: comparing for

example the lifetime of Σ0 _{in the Σ}0 _{→ Λ + π}0 _{process (τ = 10}−23_{s) with}

the electromagnetic decay Σ0 _{→ Λ + γ (τ = 10}−_{19 s), one can get the strong}

coupling constant αs: αs αe = (10 −19 10−23) 1/2_{' 10}2_{, α} s= g2 4π ' 1 , (1.9) where g is the value of the strong charge.

In order to explain the existence of hadrons made up of three quarks of the same avour and quantum numbers, a new charge type has been inserted, the colour [3]. According to the Pauli's principle, the colour can assume three possible values called red, green and blue (R, G, B), making the total wavefunction of those hadrons antisymmetric. Only quarks carry colour charge, that means that only quarks are aected by the strong force. Moreover the interquark interactions are assumed to be invariant under colour interchange, meaning that the theory is described by the symmetry group SU(3). Colour symmetry is supposed to be exact, therefore the strong interaction is independent of the quark colours involved.

QCD invariance under global gauge transformations leads to the colour charge conservation. In order to guarantee the local gauge invariance, one should introduce a covariant derivative

Dα= ∂α+ igtA·AAα(x) , (1.10)

where AA

α is the proper gauge eld of the strong interaction, the gluon, and

tA is a matrix in the fundamental representation of SU(3). The eld strength

tensor FA

αβ can be expressed in function of the gluon eld AAα:

F_αβA = [∂αAAβ − ∂βAAα − gf

ABC_AB αA

C

β] , (1.11)

where indices A, B, C run over the eight colour degrees of freedom of the gluon eld. The third therm in Eq.(1.11) is a typical feature of a non-abelian theory: it gives rise to triplet and quartic gluon self-interactions (see Fig.1.5); fABC

are the structure constants of the SU(3) colour group. The Lagrangian of the strong interaction is L = X f lavours ¯ qa(iγµDµ− m)abqb− 1 4F A αβF αβ A . (1.12)

It does not contain a m2_Aα_A

α, that should represent the gluon mass but is

not invariant under local gauge transformations.

In order to deeply understand the strong interaction, let me spend some words on its main features. Fist of all, the strong coupling constant is a function of energy, as the ne constant (see Fig.1.4). The quark-antiquark pairs coming out of vacuum shield the colour charge, reducing its value for increasing dis-tance, or for increasing momentum transferred in the process. However the action of gluons is a smearing of the colour charge, which results in an oppo-site eect of that of quarks called antiscreening (Politzer, Gross and Wilezek, 1973 [9]).

Figure 1.4: Comparison between electromagnetic and strong coupling constants.

What happens is that all around an isolate quark, all the vacuum pulsates; quark-antiquarks pairs create and then disappear, gluons appear and then fade away. This cloud of virtual particles antiscreens the central quark, making the colour charge grow with increasing distance from the quark. Nevertheless it would require an innite energy. This divergence can be avoided if near a quark its antiquark is present, because they neutralise each other. Therefore neither quarks, nor antiquarks, nor pairs can exist alone.

can be dened

ΛQCD(nf) = µ2exp[−

12π

(33 − 2nf)αs(µ2)

] , (1.13) where µ2 _{is the energy scale and n}

f is the number of avours which contribute

to the strong process. ΛQCD represents the scale at which the coupling would

diverge: more qualitative, it indicates the order of magnitude at which the strong coupling constant becomes strong. This is an indication of conne-ment, the mechanism that keeps quarks and antiquaks together inside hadrons [9]. Connement explains why the quark and the gluon degrees of freedom have never been observed as free particles, which is actually a consequence of the growth of the strong coupling constant at low energies. On the other hand, when the momentum transferred is large, namely when two quarks are really close, their interaction is feeble: this property is called asymphtotic free-dom. Fig.1.5 illustrates the fundamental Feynman diagrams for the strong interactions.

Figure 1.5: Feynman QCD diagrams: from the right the exchange of a gluon by two quarks and triplet and quartic gluon self-interactions are shown.

1.2 The top quark

The discovery of the top quark was made possible by the remarkable success of D0 and CDF experiments at Tevatron p¯p collider [10]-[11]. Based on data collected in 1994-1995 at a 67 pb−1 _{and 44-56 pb}−1 _{integral luminosity for CDF}

series of triumphs of the Standard Model. In fact the top quark is the last fundamental quark that has been discovered; with a charge +2/3 |e| and a weak isospin +1/2, it is the partner of the b-quark in the third weak doublet. Its existence was predicted many years before the experimental evidence, after the discovery of the b-quark in 1977. Its mass of mt = 173.2 ± 0.9 GeV [12],

makes the top the heaviest of the six known quarks of the Standard Model. It is one of the fundamental parameters of the theory, because it appears in higher order loop diagrams of the electroweak theory. The large value of mt also implies a large coupling with the Higgs boson: therefore the Yukawa

coupling yt = mt/v, where v = 246 GeV is the vacuum expectation value, is

of order of unity. Moreover the full decay width of the top quark is measured to be 1.33 GeV, implying a very short life time of about τ = 0.5 · 10−24_{s, if}

compared to the hadronization timescale of τhad= 3 · 10−24s. Top is indeed the

only quark of the SM with the property of decaying weakly (t → W b) before hadronizing and oers a unique opportunity to study the properties of a bare quark, including polarisation eects. For these reasons the top quark plays a special role in the Standard Model: an accurate knowledge of its features can be a key on the fundamental interactions at the electroweak breaking scale and beyond.

1.2.1 Top pair production

Because of its large mass, the top quark can only be observed directly in high energy experiments, where suciently high center-of-mass energies have been achieved. Signicantly high energy has been reached at Tevatron (√s = 1.8 TeV) and LHC (√s = 14 TeV) hadron colliders.

According to the Standard Model, the dominant mechanism for the top pair production is governed by the strong interaction: since mt >> ΛQCD, the t¯t

production can be successfully described by the perturbative QCD theory. The two main production channels at the leading order (LO) are quark-antiquark annihilation (qq → t¯t) and gluon-gluon fusion (gg → t¯t), while at next-to-leading order (NLO) there are also partonic sub-processes with gq (g¯q) in the

initial state. Fig.1.6 shows the leading order diagrams for top pair production. Approximately 85% of the production cross section at the Tevatron is from q ¯q annihilation [13], because the contribution of the valence quarks of the initial state favoured at that center-of-mass energy with respect to the gluon contribution. On the other hand at LHC about 90% of the production is from gluon-gluon fusion [14] because of the large gluon density in the proton at small x; the remainder is determined by the quark-antiquark annihilation. At both colliders the gq (g¯q) processes contribute only at the percent level. At LHC the total t¯t cross section is 172.0+6.4

−7.5 pb at

√

s = 7 TeV and 254.8+8.8_−7.5pb at√s = 7TeV, which represents about 2/3 of all events containing top quarks.

Figure 1.6: Gluon-gluon fusion and quark-antiquark annihilation Feynman diagrams for t¯t production at leading order QCD.

1.2.2 Single top production

The responsible for the single top production is the electroweak interaction through the vertex W tb (about 100% of all cases since |Vtb| >> |Vtd|, |Vts|).

The production cross section is predicted to be σt = 20pb at

√

s = 7 TeV pp collisions, smaller than that for pair production [16]. The experimental signature of this process suers from much more challenging background con-tamination; indeed the observation of single top quark production was only made in 2009 at D0 and CDF.

There are three dierent single top production processes distinguished by the virtuality of the W boson exchanged: the t-channel, the tW-channel and the s-channel, illustrated in Fig.1.8. At Tevatron, the signicant channels were the t- and the s-channel, with a production cross section of about 2.2 pb and

Figure 1.7: Theoretical Inclusive t¯t production cross section predicted for LHC and comparison between ATLAS, CMS, D0 and CDF measurements. LHC energy 4 times greater than that of the Tevatron corresponds to a top pair cross section 30 times greater [15].

1 pb respectively. Associated production with a W boson, although signicant at the LHC, was negligible at Tevatron. A further analysis on the kinema-tics of dierent production processes al LHC follows (Tab.1.4). The s-channel process has the smallest cross section at LHC (σt < 26.5(20.5) pb, about ve

times larger than the SM expectations). In this production mode a time-like W boson is produced from two quarks belonging to an isospin doublet. Next in order of increasing cross section is the associated production of a top quark and a W boson, in which a initial state bottom quark emits W boson (σt = 14.4+5.3−5.1(stat.)+9.7−9.4(syst.) pb). The t-channel is the predominant single

top production mode, accounting about 3/4 of single top quarks produced at LHC (σt = 83 ± 4(stat.)+20−19(syst.) pb). In this process, a space-like W boson

scatters with a b-quark, coming from the b-quark PDF of the proton or pro-duced by gluon splitting g → b¯b. At proton-proton colliders the t-channel is a charge asymmetric process, due to the prevalence of u type valance quarks in the proton PDF.

All of the production modes are sensitive to the W tb vertex in dierent ways: indeed non-standard couplings would indicate the presence of some new phy-sical phenomena. In addiction the single top production allows to directly measure the CKM matrix element, without hypothesize the number of genera-tions; deviations from the Standard Model expectations could be a signal for other generations of quarks.

Table 1.4: Expected single top quark production cross sections in dierent channels at a center-of-mass energy of 7 TeV and 8 TeV, given by approximate NNLO assuming mt= 172.5 GeV [2].

Production mode σt[pb] 7 TeV σt[pb]8 TeV

s-channel 4.6 ± 0.2 5.6 ± 0.2 t-channel 64.6+2.7_−2.0 87.8+3.4_−1.9 tW-channel 15.7 ± 1.1 22.4 ± 1.5

Figure 1.8: Leading-order Feynman diagrams for s-channel, t-channel and associated production with W boson.

1.2.3 Top decay

According to the the Standard Model, a vast majority of the top quarks decays into a W boson and a b-quark through the electroweak process. The width of such a decay is proportional to the square of the element in the Cabibbo-Kobayashi-Maskawa matrix (CKM). Since |Vtb| >> |Vtd| , |Vts| (see Eq.1.1.2),

decays to the other down-type quarks, s and d, are suppressed. Neglecting the decays t → W d(s), the total width of the top quark in the SM at NLO QCD is [17]: Γt= GFm3t 8π√2|Vtb| 2_{(1 −} m2W m2 t )2(1 + 2m 2 W m2 t )[1 − 2αs 3π ( 2π2 3 − 5 2)] , (1.14) where GF is the Fermi constant, mW is the mass of the W boson, mt is the

mass of the top quark and αsis the strong interaction coupling (here αs(MZ) =

0.118). For a top mass of 172.5 GeV , the decay width of this vertex yields Γt =

1.33 GeV, which corresponds to a very short lifetime τt = 1/Γt ∼ 5 · 10−25s.

The fact that the top lifetime is one order of magnitude smaller than the typical formation time of hadrons means that top quark decays before hadronize. It is also an explanation of the absence of bound states containing top quarks (e.g. toponium). The top quark mass is even larger than the sum of the W boson (Tab.1.3) and b-quark (Tab.1.2); this implies that the W boson belonging from this decay is "on-shell". This is an important feature of t¯t events that makes the precision measurements of the top quark mass possible.

The top quark pairs decay modes are classied according to the decay of the W boson [16]: di-leptonic, lepton+jets and hadronic channels (see Fig.1.9 and Fig.1.10). The experimental signature varies in the dierent channels; the event topology and the background processes are summarized in Tab.1.5. In the di-leptonic channel both the W-bosons decay into lepton-neutrino pairs t¯t → W+bW−¯b → ¯lνlbl

0

¯

ν_l0¯b. The presence of two isolated high p_T leptons, a

huge missing energy and at least two b-jets permits to easily identify this event, even if the two neutrinos make the reconstruction dicult. The branching ratio is small (BR = 10.3%), but the backgrounds (mostly Z+jets), are also fairly small. This makes the di-leptonic topology a valid process to obtain a very clean sample of t¯t events. On the other hand, in the lepton+jets channel one W-boson decays into lepton and neutrino, while the other one into a quark-antiquark pair t¯t → W+_bW−_{¯b → q ¯q}0

bl ¯νl¯b (or ¯lνlbq ¯q

0_¯

b). Its signature is one high pT isolated lepton, missing transverse energy and at least 4 jets: with a

channel is often referred as the golden channel. Finally, the hadronic channel is characterized by the decay of both the W bosons into quark-antiquark pairs t¯t → W+_bW−_{¯b → q ¯q}0

bq00q¯000¯b. The typical signature is the presence of six jets, whose two belong to the b quark. Despite the large branching ratio (46.2%), the observation of this process is dicult by the presence of QCD multi-jets events not involving top quark.

Figure 1.9: Illustration of dierent top pair production and decay modes.

Table 1.5: Summary of main signatures and background of the three t¯t decay chan-nels.

Channel Event topology Dominate background Dileptonic 2 b-jets, 2 isolated leptons, Emiss

T Z + jets

Lepton+jets 2 jets + 2 b-jets, 1 isolated leptons, Emiss

T W + jets

Hadronic 4 jets + 2 b-jets, no isolated leptons, no Emiss

Figure 1.10: Top pair decay channels (right) and the corresponding branching-ratios (left).

1.2.4 Top quark mass

The top quark mass is a fundamental parameter of the Standard Model. A precise determination of this value induces large corrections in the theory pre-dictions of many precision electroweak observables, including the mass of the Higgs boson. The top quark mass has been measured in the lepton+jets, dileptonic and hadronic channels by Tevatron and LHC experiments [16] (see Fig.1.11). The most precise measurement of the top quark mass was made by Tevatron [2]

mt= 173.20 ± 0.51(stat.) ± 0.71(sist.) GeV /c2 ;

with a relative precision is 0.50%, it is a combination of Run I and Run II measurements based on data set corresponding to a luminosity of 8.7 fb−1_.

Indirect constraints on mt can be obtained from precision measurements of

electroweak theory. In fact the mass of the W-boson can be expressed as a function of the QED coupling α(m2

Z), the Fermi constant GF and the

electro-weak mixing angle θW

m2_W = πα(m 2 Z)/ √ 2GF sin2_θ W · (1 − δr) . (1.15)

The term δr contains contributions from higher order electroweak loop

dia-grams involving the square of the top quark mass mt.

Figure 1.11: Overview of the top mass measurements from both ATLAS and CMS in the lepton+jets, dileptonic and hadronic channels [12].

1.3 Cross section measurements

In order to quantify particle production, it is important to evaluate the cross section of the process under consideration, that is a measure of the interaction probability. In high energy colliders such as LHC, protons can scatter and produce other particles; all those possible processes are described by the total inclusive cross section. On the other hand the exclusive cross section is the probability for a process to happen. The total cross section formula for a collision is given by

σ = Nev

where Nev is the number of scattered events,  is the overall eciency of the

detector and L is the luminosity of the acquired data, meaning the luminos-ity obtained during the data acquisition. The instantaneous luminosluminos-ity for a collider is given by

L = f · N n1n2

4πσxσy

, (1.17)

where f is the collision frequency, n1 and n2 are the number of particles

be-longing to a bunch of the beam, N is the number of bunches and σx and σy are

the transverse dimensions of the bunch along two orthogonal axis with respect to the beam direction.

At LHC energies, interactions happen among partons, the elementary parti-cles (quarks and gluons) inside the proton which participate to the process almost independently. As a consequence, the available energy is the fraction of the center-of-mass energy carried by partons: pq,g = xPp, where x is called

Bjorken variable. It varies between 0 and 1 and represents the fraction of the total momentum carried by the parton. The distribution of the momentum among all partons inside the proton is described by the Parton Distribution Functions (PDF), determined trough the combination of a large amount of experimental data on deep-inelastic scattering. The inclusive cross section of the process pp → t¯t strongly depends on the center-of-mass energy of the col-lider and on the top mass; it can be expressed by means of the factorization theorem, which allows to convolute the parton distribution function and the partonic cross sections ˆs:

σpp→t¯t(s, mt) = X i,j=q,¯q,g Z dxidxjfi(xi, µ2f)fj(xj, µ2f)ˆσij→t¯t(ˆs, mt, µfµr, αs) . (1.18) The sum runs over all the quarks and gluons which contribute to the process, xi,j are the parton momentum fraction with respect to the proton momenta,

fi,j(xi,j, µ2f)are the proton PDF, µ2f and µ2rare the factorization and

renormali-zation scales, αsis is the strong coupling constant and ˆs ∼ xixjsis the partonic

center-of-mass energy. The dependence from µr arises from the denition of

theory; on the other hand, µf indicates a transition between the perturbative

and the non pertubative regime, thus arises from absorbing collinear initial state singularities in the PDF. The renormalization and factorization scale are usually set to the hard scale of the process: in the case of the total cross section, one usually sets µr = µf = mt. However in the case of the dierential

cross sections, other scale choices are more appropriated (e.g. the transverse momentum of a jet pT ,jet or the top pair invariant mass Mt¯t).

1.3.1 t¯t total cross section

The top pair cross section was rst measured in p¯p collisions at Tevatron with a center-of-mass energy of √s = 1.96 TeV. The most precise and recent measurements of D0 and CDF are

σD0 t¯t = 7.56 +0.63 −0.56 pb σCDF t¯t = 7.50 ± 0.48 pb

in agreement with the Standard Model expected value of σt¯t = 7.16+0.20−0.23 pb

at NNLO perturbation theory [16]. The strong dependence on the collision energy, explains why the theoretical production cross section at LHC is far greater than the Tevatron one. In particular at the center-of-mass energy of √

7 TeV and√8 TeV, the SM predicted values are respectively σ7T eV_t¯t = 172.0+6.4_−7.5 pb

σ8T eV

t¯t = 254.8 +8.8

−7.5 pb .

ATLAS and CMS evaluated the top pair production cross section combining measurements performed in various channels. It follows a brief summary of the results in both ATLAS and CMS [2] at the center-of-mass energy of 7 TeV and 8 TeV respectively (see also Fig.1.12).

σ_t¯AT LAS(7T eV )_t = 173 ± 3(stat.)+8−4(syst.) ± 7(lumi.) pb

σ_t¯CM S(7T eV )_t = 162 ± 2(stat.) ± 5(syst.) ± 4(lumi.) pb

σ_t¯AT LAS(8T eV )_t = 237.7 ± 1.7(stat.) ± 7.4(syst.) ± 7.4(lumi.) pb σ_t¯CM S(8T eV )_t = 227 ± 3(stat.) ± 11(syst.) ± 10(lumi.) pb .

Figure 1.12: Summary of the ATLAS and CMS most precise measurements of top-antitop pair per decay mode, compared with several theory predictions at NLO and NNLO QCD [2].

These results are in agreement with NNLO Standard Model perturbation theory as it is shown in Fig1.7.

1.3.2 Dierential cross section

The large abundance of top quark pair production at LHC allows not only to measure the total cross section σt¯t, but also the dierential cross section

dσt¯t/dX, where X is a relevant variable, such as the kinematic variables of the

t¯t system. In fact cross section can be evaluated either after the extrapolation to the full phase space, as done in the case of the total cross section, or only within the kinematic range in which the decay products are measured. In particular a prominent role in the discovery of new physics have the invariant

mass distribution Mt¯t and the transverse momentum pT,t¯t, which could be

signicantly modied in presence of resonances decayed in top pairs.

In order to compare dierential cross section measurements with theoretical predictions, it is important to clarify two dierent way to quote it: the particle level that considers only particles visible by the detector and easily comparable to Monte Carlo simulations, or the parton level which refers to particle before hadronisazion.

Thanks to the large available event samples, Tevatron and LHC performed rst dierential cross section measurements in top-antitop production [2]. Such measurements allow accurate tests on perturbative QCD, the extractions or the use of PDFs and enhance the sensitivity to possible new physics contributions. In particular both ATLAS and CMS performed several measurements with increasing statistic on dierent channels. Fig.1.13 shows a recent study of ATLAS collaboration in the lepton+jets channel; the result was obtained at an integrated luminosity of 2.6 fb−1 _{in the resolved channel. This was possible}

due to the fact that the analysis was focused the top pair with pT only up to 1

GeV. The aim of this thesis instead is to extend the top pair production analysis to the highest energy regions, where new physics states may be found. In the reconstruction of high pT top quarks (boosted top), standard techniques fail

because of the partial or total overlap of its decay products, which form a huge signal (fat-jet) in the detector. In this context the Template Overlap Method (TOM) becomes necessary. TOM oers a new top tagging strategy based on the comparison of the fat-jet with a series of top decay states (templates) generated through Monte Carlo simulations. The comparison is based on a denition of an overlap function which quanties the matching. Further details are provided in Chapter 3.

1.4 Beyond Standard Model

For the past few decades physicists have made measurements of particles and parameters of the Standard Model; provided the discovery of the Higgs boson

Figure 1.13: Lepton+jets channel normalised dierential t¯t production cross sec-tion obtained by the ATLAS collaborasec-tion as a funcsec-tion of Mt¯t, pT,t¯t and yt¯t. The

measurements is compared to the NLO prediction from MCFM [18].

and excluding the discovery of neutrino masses, no major deviations from the SM predictions have been found. Despite the remarkable success of the theory, there remain many unresolved questions that lead physicists to look beyond the Standard Model.

The structure of the SM is itself a deep mystery. The gauge groups that de-scribe the various interactions seem to adequately dede-scribe nature, but why should nature choose these groups instead of others? Similarly, many param-eters of the theory, as the coupling constants or the particle masses, are free parameters and have been evaluated from experiments. Theoretical problems can arise from the values of some of them: the hierarchy problem and the vacuum expectation value of the Higgs potential, which inuences the W and Z masses, are some issues.

Another set of questions concerns major problems in physics that the SM does not address. First among these is the inability to integrate a theory of gravity in a consistent manner: this is a general problem of quantum eld theories, as no renormalizable quantum eld theory of gravity has been forthcoming. Moreover the expansion of the universe due to the dark energy phenomenon and the presence in the universe of the dark matter, have no explanation in the Standard Model. Furthermore the Standard Model is not sucient to ex-plain the observed asymmetry between matter and antimatter in nature: the CKM matrix predicts some CP violations which lead to this imbalance, but the known sources of CP violations are insucient to account for this large discrepancy.

There are many scenarios of physics beyond the SM which involve top quarks [16]. One of them predicts new interactions with enhanced coupling to the top quark, resulting in new particles that would decay into t¯t pairs and may show up as resonances in the top-quark pair invariant mass distributions. New interactions imply the possible presence of new gauge bosons, as W0

and Z0

, the heavier counterpart of the W and Z of the electroweak theory. At the moment no sign from new physics has been found in the Mt¯t distribution and

new heavy resonances decaying into t¯t pairs have been excluded for masses up around 1.5 TeV.

Extended models add two charged Higgs bosons to the SM, which may be heavier or lighter than the top quark. In the case of a charged Higgs heavier than the top quark, an additional diagram would be added to t-channel pro-duction through the replacement of the W boson by a charged Higgs boson; although the impact on the t-channel cross section would be small, making this an unpromising discovery channel for charged Higgs. A charged Higgs lighter than the top quark would introduce additional diagrams contributing to t-channel production, but since the Higgs couples preferentially to massive particles the eect would be suppressed by the small coupling between the charged Higgs and the light quark in the initial state. The principal experi-mental clue for such a particle would be the introduction of a new decay mode

for the top quark.

In addiction, model independent studies can be carried out to search for non standard model interactions; they may be parametrized via eective eld the-ories that allow the existence of avour changing neutral current (FCNC) pro-cesses such as cq → tq or qq → Z → tc. Researches for FCNC top quark decay and production, same sign top quark production, fourth generation of quarks, charged Higgs and W0 _{so far have turned out negative, but can already}

provided more stringent exclusion limits.

Finally an other problem concerning the Standard Model is the non unica-tion of the electroweak and strong interacunica-tions: the theory that unies these three forces is called Grand Unication Theory (GUT). One of the most po-pular extensions to the SM is Supersymmetry (SUSY) based on the Poincaré group U(1) ⊗ SU(2) ⊗ SU(3). The basic idea behind SUSY is a symmetry be-tween fermions and bosons, in such a way that every SM fermion should have a super partner boson and vice-verse. SUSY may provide particles that can solve the problem of the grand unication: it predicts an energy scale where all the interaction coupling constants meet. At the moment there are no ex-perimental conrmations of supersymmetric particles; the symmetry between particles and their superpartner must be broken. This leads to the prediction of a superparticles mass much larger than the SM masses. Operating from March 2015 at the center-of-mass energy of √14 TeV, LHC Run II will oer a great possibility to explore energy regimes never reached so far, in the hope to observe new physics.

LHC and ATLAS

2.1 LHC

The Large Hadron Collider (LHC) is the largest particle accelerator in the world. Located at CERN, beneath Franco-Swiss border near Geneva, it has been built in the same tunnel which hosted the former Large Electron-Positron (LEP) collider. The tunnel has a circumference of 27 km [19] and it is situated between 50 and 175 m under ground. LHC is a proton-proton collider with a design center-of-mass energy of 14 TeV at a peak luminosity of 1034_cm−2_s−1_.

It can also work as a lead ion collider, accelerating fully ionized leads atom at a center-of-mass energy of 1150 TeV (∼ 2.76 TeV/nucleon) and at a luminosity of 1027_cm−2_s−1_{. It started be operating in 2008 and during 2010 and 2011}

it reached the center-of-mass energy of √s = 7 T eV; in 2012, the center-of-mass energy has been increased until 8 TeV, with a maximum luminosity of L = 4 · 1033_cm−2_s−1 _{[19]. After a technical shut-down period of two years,}

LHC will start operating again at energies approaching its design parameters in March 2015. The high energy and luminosity will oer the opportunity for both precision measurements and high energy frontier explorations.

In the LHC tunnel two proton beams circulate in opposite directions into two separate ultra-high vacuum chambers at a pressure of 10−10 _{Torr. In}

or-der to keep the beams into circular trajectories, 1232 NbTi superconducting

dipole magnets produce a magnetic eld of 8.4 T; other 392 superconducting quadrupole magnets generate a eld of 6.8 T necessary to focalize the beams. The superconducting magnets are cooled with superuid helium below 2 K. The magnet systems use a twin bore design to bend particles in both beams simultaneously, which collide every 25 ns.

Beams are not continuous, but are divided into a maximum of 2808 bunches gathered in trains of 80; moreover each bunch contains 1011_{protons which give}

rise to 109 collisions per second, assuming a total proton-proton cross section

of 10−25_cm2 _{at the LHC energy [20]. The most important LHC parameters are}

reported in Tab.2.1.

LHC protons are originated from ionised hydrogen and passed through a chain

Table 2.1: LHC technical parameters for 2012.

Maximum collision energy 8 TeV Maximum Luminosity 2.3 · 1034_cm−2_s−1

Number of particles per bunch 1.67 · 1011

Number of ll bunches 2808 Bunch separation 25 ns Bunch length 7.7 cm Bunch width (Atlas) 16.7 µm Total number of particles 4.7 · 1014

Mean current 0.584 A Number of collision per bunch 25

of accelerators of progressively grater energy before entering in the beam-pipe (Fig.2.1). The process begin with the LINAC2, a linear accelerator which increases the proton energy to 50 MeV. The following three stages are syn-chrotrons: the Proton Synchrotron Booster (PSB) leads protons to 1.4 GeV, the Proton Synchrotron (PS) to 25 GeV and the Super Proton Synchrotron (SPS) to 450 GeV. In the LHC ring beams are further accelerated by 16 ra-diofrequency cavities with a maximum electric eld of 5.5 MV/m.

Four interaction regions along the tunnel host the following experiments, as shown in Fig.2.1:

Figure 2.1: Schematic view of CERN accelerators.

ˆ ATLAS (A Toroidal LHC ApparatuS) is a multi-purpose experi-ment which works at high luminosity (L = 1034_cm−2_s−1_{) to explore the}

Higgs boson and all the heavy particles, that may permit to solve the mass origin and the extradimension problems.

ˆ CMS (Compact Muon Solenoid) is a multi-purpose experiment de-signed to work up to the same high luminosity of ATLAS, but imple-mented with dierent and complementary technologies.

ˆ LHCb performs accurate measurements of the b-quark physics (e.g. CP violation of B mesons). It works at a luminosity lower than the one designed for the two previous experiments (L = 1032_cm−2_s−1_{), in order}

to better reconstruct the decay vertices of B-mesons, made dicult when there is more than one interaction per bunch crossing.

ˆ ALICE (A Large Ion Collider Experiment) is dedicated to the study of heavy ion collisions, in order to reproduce the matter state

(called Quark-Gluon Plasma) for the rst 30 µs of its life, that means early after the Big Bang. Due to the high nucleus-nucleus cross section, ALICE works up to luminosities of L = 1027_cm−2_s−1_.

2.2 ATLAS

ATLAS is multi-purpose particle detector installed 100 m underground in the interaction Point 1, along the LHC tunnel. With a total length of 42 m, a diameter of 22 m and a weight of 7000 t, it is the most extended of the LHC experiments [21]. The detector is organized in a central barrel and two end-caps that close both ends. It has a cylindrical symmetry around the beam pipe: all of its subdetectors are arranged in concentric layers around the interaction point, each optimized to the detection of a specic type of particles. ATLAS is composed by six main subsystems:

ˆ the Magnetic System, it is necessary in order to bend the trajectory of charged particles and to measure their momentum;

ˆ the Inner Detector, that provides precise measurements of the traje-ctory of charged particles and reconstructs the interaction vertexes; ˆ the Electromagnetic and the Hadronic Calorimeter, optimized for

the measurement of the photon and electron energy and jets of hadrons, respectively.

ˆ the Muon Spectometer, specialized apparatus which identies muons and measures their energy. Muons are indeed very penetrating particles which cross all the previous subdetectors without losing their energy, but leaving only an ionization signal;

ˆ the forward detectors, among which LUCID, nalized to the luminosity measurement.

Figure 2.2: The ATLAS detector.

coordinate system is dened with respect to the interaction point, around which the detector is forward-backward symmetric [21]. The beam direction identies the z-axis and the x-y transverse plane. According to the standard convention, the positive x-axis is dened as pointing to the center of the LHC ring, while the positive y-axis is dened as pointing upwards from the beam. Keeping in mind the cylindrical symmetry of ATLAS, the spherical (r, φ, θ) coordinate system is frequently employed, where r is the radius from the central axis, φ is the azimuthal angle measured around the beam direction and θ is the polar angle from the beam axis. As a function of θ, the pseudorapidity describes the angular position relative to the beam axis

η = −ln tan(θ/2) ; (2.1) in the non zero approximation for highly relativistic particles, this denition closely approximates the denition of rapidity

y = 1 2ln(

E + pz

E − pz

The transverse momentum pT, the transverse energy ET and the missing

trans-verse energy Emiss

T are dened in the x-y plane. The distance between two

objects in the pseudorapidity-azimuthal plane (η, φ) is

∆R =p(∆η)2_{+ (∆φ)}2 _. (2.3)

Figure 2.3: Section of ATLAS detector.

2.2.1 The magnets system

The magnets system is nalized to the evaluation of the charge q and the momentum p [GeV/c] of particles, through the measurement of the curvature radius ρ [m] of their trajectories, when they cross a region with a magnetic eld B[T ]:

p = 0.3 ρ q B . (2.4) ATLAS is characterized by three dierent superconductive magnetic systems:

• Central Solenoid (CS): installed around the Inner Detector, it is a

superconducting solenoid of a niobium-titanium (NbTi) alloy. With a radius of 1.2 m and a length of 5.3 m, it carries a 8 kA current to provide a magnetic eld of 2 T. The coil is kept at a temperature of 4.5 K by a ux of liquid helium. CS is represented in blue in Fig.2.4.

• Barrel Toroid (BT): it is composed by 8 rectangular superconducting

coils arranged in a cylindrical conguration and kept at a temperature of 4.5 K. The total length is 25 m, the outer diameter is 20.1 m and the inner diameter is 9.4 m. Installed just outside the calorimeters, it bends particles with η ≤ 1 and provides a magnetic eld of 1.5 T.

• End-Cap Toroid (ECT): it is composed by 8 rectangular coils arranged

in a single cylindrical vessel. The total length is 5 m, the outer diameter is 10.7 m and the inner diameter is 1.65 m. The vessel is mounted at the end of ATLAS in order to close the magnetic eld lines produced by the Barrel Toroid. The 2 T magnetic eld is orthogonal to the beam axis and bends particles emitted at small polar angle (1.4 < η < 2.7). The entire Toroid Magnets (in red in Fig.2.4) reach a total magnetic eld of 4 T mostly orthogonal to muon trajectories.

Figure 2.4: The Central Solenoid (blue), the Barrel Toroid and the End-Cap Toroids (red) of the magnetic system.

2.2.2 Inner Detector

The Inner Detector (ID) is the part of the apparatus closest to the beam pipe; it is placed in a cavity delimited by calorimeter cryostats around the beam pipe. It reconstructs the charged particle tracks by measuring the ionization energy they produce as they move through the detector medium. It has an inner radius of 45 mm, an outer radius of 115 cm and a length of 6.2 m. The ID is immersed in a 2 T magnetic eld parallel to the beam axis. Its struc-ture is composed by two silicon revelation systems, the Pixel Detector and the SemiConductor Tracker (SCT), and by a Transition Radiation Tracker (TRT), as presented in Fig.2.5 and Fig.2.6.

The two major goals of track reconstruction are the measurement of momen-tum and the reconstruction of interaction vertexes. The momenmomen-tum can be inferred by measuring the curvature of the tracks produced as charged parti-cles move through the eld; on the other hand, interaction vertexes are recon-structed by extrapolating tracks recorded in the ID to their origin point in the beam pipe. This process is essential to reject pile-up and to tag jets produced by the decay of heavy particles. The Inner detector provides a transverse mo-mentum resolution of about 4% for 100 GeV muons and a transverse impact parameter resolution of ∼ 35 µm for pT = 100 GeV and ∼ 10 µm for pT = 5

GeV pions. At designed luminosity, about 1000 charged particles are expected every 25 ns within the coverage of the tracking detectors, which extends out to |η| < 2.5 [20].

Pixel Detector

It is the innermost tracking detector made up of silicon pixel with high granu-larity. Therefore it is designed to measure the particle impact parameters, the production vertexes and the decay of short lived particles, as B mesons or τ leptons. The pixel detector consists of three concentric layers around the beam axis at average radii of 5 cm, 9 cm and 12 cm and ve rings perpendicular to the beam axis on each side of the interaction point (11 cm inner radius and 20 cm outer radius) [22]. It is composed by 1744 modules, each consisting

Figure 2.5: An illustration of the ATLAS Inner Detector. It highlights the major features of the design, showing the arrangement of modules in the barrel and end-caps of the Pixel Detector, the SCT and the TRT.

of a 250 µm layer of silicon pixels, adding up to a total of 80 million pixels. The system occupies a total area of 1.73 m2 _{and has an intrinsic accuracy in}

the position determination of 10 µm in the r − φ plane and 115 µm in the z direction for the barrel detector, while an accuracy of 10 µm in z − φ and 115 µm in r for the end-caps.

SemiConductor Tracker (SCT)

Placed in the intermediate radial range of the ID, the SCT provides precise reconstruction of tracks and measurements of momentum, impact parameter and vertex position [23]. It employs the same semiconductor technology as the Pixel Detector, with the dierence in the use of silicon microstrips instead of pixels systems. The SCT consists of four double layers in the barrel region and nine end-cap disks per side that cover up to |η| < 2.5: each of the 4088 detector

modules incorporates two layers with the strips rotated of 40 mrad one with respect to the other; information from both layers allows the reconstruction of a precise hit location. It occupies an area of 63 m2 _{and has a spatial resolution}

of 17 µm along the r − φ plane and 580 µm in the z direction; moreover SCT provides a transverse momentum resolution of about 4% for 100 GeV pions. Its high granularity is important for the pattern recognition.

Figure 2.6: cross sectional view of the Inner Detector.

Transition Radiation Tracker (TRT)

It is the outer component of the Inner Detector and participates to the track reconstruction and to the momentum measurement in the |η| < 2 region. It is equipped with continuous tracking elements, based on the use of straw de-tectors. Each straw is 4 mm in diameter for a maximum straw length of 144 cm in the barrel [24]. A gold-plated tungsten wire in the middle of each tube collects the signal. Filled with a ionizing gas mixture of 70% Xe, 20% CO2